Algebra | A.P., G.P., H.P.: Definitions; General term; Summation of series |
Logarithms: Definition; Properties; Change of base |
Complex Numbers: Definition; Properties; Complex conjugate; Triangle inequality; De Moivre’s theorem |
Polynomial equation: nth degree equation; Quadratic Equations with real coefficients |
Permutation and Combination: Basic properties; Problems involving permutations and combinations |
Principle of Mathematical Induction: Sum of squares and cubes; Divisibility properties |
Binomial theorem: Statement; General term; Properties of binomial coefficients |
Matrices: Concepts; Operations; Determinants; Inverse of a matrix; Solutions of system of linear equations |
Sets, Relations, and Mappings: Idea of sets; Venn diagram; Equivalence relation; Mappings |
Statistics and Probability | Measure of dispersion; Mean, variance, and standard deviation; Probability rules; Binomial distribution |
Trigonometry | Trigonometric functions; Addition and subtraction formulae; General solution of trigonometric equations |
Properties of triangles; Inverse trigonometric functions and their properties |
Coordinate Geometry of Two Dimensions | Distance formula; Section formula; Condition of collinearity; Equation of lines; Angle bisector |
Equation of a circle; Condition that a general equation may represent a circle; Parametric equation of a circle |
Definition of conic section; Equation of Parabola, Ellipse, and Hyperbola in standard form |
Coordinate Geometry of Three Dimensions | Direction cosines and direction ratios; Equation of a straight line; Equation of a plane; Distance formula |
Calculus | Differential calculus: Functions; Limit, continuity, derivative; Rolle’s Theorem; L’Hospital’s rule |
Integral calculus: Indefinite integral; Integration by parts and substitution; Fundamental theorem of integral calculus |
Differential Equations: Formation; Solution methods |
Application of Calculus: Tangents and normals; Maxima and minima; Motion in a straight line; Area calculation |
Vectors | Addition of vectors; Scalar multiplication; Dot and cross products; Scalar triple product |
